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For a molecule with 2 chiral centres, there are four possible combinations, (R,R), (R,S), (S,R) and (S,S). For example, 3-bromo-2-butanol has four stereoisomers: (2R,3R)-3-bromo-2-butanol, (2R,3S)-3-bromo-2-butanol, (2S,3R)-3-bromo-2-butanol and (2S,3S)-3-bromo-2-butanol.

Of these combinations, the following pairs are diastereomers:

S,R and S,S

S,R and R,R

R,S and S,S

R,S and R,R

I notice that only one chiral centre has been flipped to form these pairs.

The following pairs are either enantiomers or meso compounds (e.g. for (2R,3S)-tartaric acid):

S,R and R,S

S,S and R,R

I notice that both chiral centres have been flipped to form these pairs.

Could we generalise that flipping an even number of chiral centres always gives either an enantiomer or the same molecule if it's a meso compound, and flipping an odd number of chiral centres always gives a diastereomer?

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Could we generalise that flipping an even number of chiral centres always gives either an enantiomer or the same molecule if it's a meso compound, and flipping an odd number of chiral centres always gives a diastereomer?

No. The generalization is slightly different: Comparing chiral centers in two stereoisomers with more than two chiral centres, if

  • all chiral centres are the same, it is the same molecule.
  • some but not all are switched, it is a diastereomer.
  • all are switched, it is an enantiomer (or meso compound).

Open-chain carbohydrates are a good example (compare D-glucose, L-glucose, D-galactose, D-talose etc.). For this class of molecules, there is one more term, epimer (when exactly one chiral centre is switched).

This generalization excludes the more exotic cases of stereoisomers, see e.g. Why are allenes chiral? and Why atropisomers are called conformers?

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